# algebraic topology

Published articles for algebraic topology.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## Computing Homology

DevFeed: [Computing Homology](<https://devfeed.tech/articles/computing-homology-40311.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/04/10/computing-homology/>)

Published: 2013-04-10T16:38:25Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Computing](<https://devfeed.tech/topics/computing.md>), [Code](<https://devfeed.tech/topics/code.md>), [Algorithm](<https://devfeed.tech/topics/algorithm.md>), [Collections](<https://devfeed.tech/topics/collections.md>), [.NET 11 Preview 7](<https://devfeed.tech/topics/net-11-preview-7.md>)

Tags: [algebraic-topology](<https://devfeed.tech/tags/algebraic-topology.md>), [algorithm](<https://devfeed.tech/tags/algorithm.md>), [code](<https://devfeed.tech/tags/code.md>), [collections](<https://devfeed.tech/tags/collections.md>), [computing](<https://devfeed.tech/tags/computing.md>), [homology](<https://devfeed.tech/tags/homology.md>), [linear-maps](<https://devfeed.tech/tags/linear-maps.md>), [matrices](<https://devfeed.tech/tags/matrices.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [ordering](<https://devfeed.tech/tags/ordering.md>), [row-reduction](<https://devfeed.tech/tags/row-reduction.md>), [structure](<https://devfeed.tech/tags/structure.md>)

### AI overview

This tutorial explains an algorithmic approach to computing homology for a simplicial complex. It represents chain groups and boundary homomorphisms as matrices, uses row reduction, and works through an extended example for computing H₁.

### Source excerpt

Update: the mistakes made in the code posted here are fixed and explained in a subsequent post (one minor code bug was fixed here, and a less minor conceptual bug is fixed in the linked post). In our last post in this series on topology, we defined the homology group. Specifically, we built up a topological space as a simplicial complex (a mess of triangles glued together), we defined an algebraic way to represent collections of simplices called chains as vectors in a vector space, we defined the boundary homomorphism $ \partial_k$ as a linear map on chains, and finally defined the homology groups as the quotient vector spaces